Let f(x)= 24 1+3e^−1.3x. what is the point of maximum growth rate for the logistic function f(x)? round your answer to the nearest hundredth.

(0.85,12)

Step-by-step explanation:

The point of maximum growth is at x = 0.82

Step-by-step explanation:

The given logistic function is :

By the graph which is attached below, we can see the maximum value of the logistic function is 24, and the point of maximum growth is at

The numerators are equal, so the denominators must be equal.

⇒ log 3 = -1.3·x

⇒ -0.4771 = -1.3·x

⇒ x = 0.4771/1.3

⇒ x = 0.82

Hence, The point of maximum growth is at x = 0.82

You can see the logistic curve and the point of maximum growth in the image below.

Step-by-step explanation:

The given curve is .

Let us parameterize C to obtain a vector equation for C.

We have ,   .

This is the equation of a circle( a cylinder in space) with radius, r=9 units.

The parametric equation of a circle is given by:

and

This implies that:

and

From, , we obtain, ,

A vector equation for C is;

for

Also, we have;

Since C is oriented counterclockwise as viewed from above, we can apply the Stokes' Theorem.

Thus, by Stokes' Theorem;